Cross-listing and price efficiency: An institutional explanation

Abstract

Although many of the benefits of cross-listing have been examined in prior research, potential improvements in price efficiency have received less attention. We examine the differences in price efficiencies between American depositary receipts (ADRs) of foreign firms and the shares listed in their home markets. Based on multifractal detrended fluctuation analysis (MF-DFA) of the daily price of 200 ADRs and their domestically listed shares for the period from January 2010 to June 2019, we find that ADRs, in general, show greater price efficiency than their corresponding home market shares. Furthermore, our analysis shows that firms from civil law countries, firms from countries that have low levels of minority investor protection, and firms from emerging economies experience the greatest gains in price efficiency when they list their ADRs in the US compared to firms from common law countries, firms from countries with high levels of investor protection, and firms from developed countries. Furthermore, we also find that these efficiency improvements cannot be attributed to increases in liquidity. Instead, they can be mostly explained by institutional differences. Our results suggest that firms engage in institutional borrowing when their home-country markets are institutionally deficient.

Appendix 1: Multifractal Detrended Fluctuation Analysis—MF-DFA

We describe below an algorithm of the MF-DFA method, based on Kantelhardt et al. (2002). The generalized multifractal DFA (MF-DFA) procedure consists of six steps. The first three steps are essentially identical to the conventional DFA procedure.

Step 1: We start by calculating the log returns for the time series. Then, let ${x}_{1, }{x}_{2,}\dots ,{x}_{N}$ be a series of N equidistant measurements. Given its mean value $\langle x\rangle$ we determine a new series of Y(1), …, Y(N) values given by:

$$Y\left(i\right)\equiv \sum_{k=1}^{i}\left[{x}_{k}-\langle x\rangle \right], i=1,\dots ., N.$$

(4)

Subtraction of the mean $\langle x\rangle$ is not compulsory, since it would be eliminated by the later detrending in the third step.

Step 2: Divide the series $Y\left(i\right)$ into ${N}_{s}\equiv \mathrm{int}(N/s)$ non-overlapping segments of equal length s. Since the length N of the series is often not a multiple of the considered time scale s, a short part at the end of the profile may remain. In order not to disregard this part of the series, the same procedure is repeated starting from the opposite end. Thereby, 2 ${N}_{s}$ segments are obtained altogether.

Step 3: Calculate the local trend for each of the 2${N}_{s}$ segments by a least-square fit of the series. Then determine the variance.

$${F}^{2}(s,v)\equiv \frac{1}{s}\sum_{i=1}^{s}{\left\{Y\left[\left(v-1\right)s+i\right]-{y}_{v}(i)\right\}}^{2}$$

(5)

For each segment $v, v=1, \dots ., {N}_{s}$ and

$${F}^{2}(s,v)\equiv \frac{1}{s}\sum_{i=1}^{s}{\left\{Y\left[N-\left(v-{N}_{s}\right)s+i\right]-{y}_{v}(i)\right\}}^{2}$$

(6)

For $v={N}_{s}+1, \dots , 2{N}_{s}$. Here, ${y}_{v}(i)$ is the fitting polynomial in segment $v$.

A comparison of the results for different orders of DFA allows us to estimate the type of the polynomial trend in the time series.

Step 4: Average over all segments to obtain the $q$th order fluctuation function

$${F}_{q}\left(s\right)\equiv {\left\{\frac{1}{2{N}_{s}}\sum_{v=1}^{2{N}_{s}}{\left[{F}^{2}\left(s,v\right)\right]}^\frac{q}{2}\right\}}^\frac{1}{q}$$

(7)

Where, in general, the index variable $q$ can be any real value except zero. For $q=2$, it yields the traditional DFA. We repeat steps 2–4 for different values of s. For financial time series, usually this is done for values of q from − 10 to 10.

Step 5: Determine the scaling behavior of the fluctuation functions by analyzing log–log plots ${F}_{q}(s)$ versus $s$ for each value of q.

$${F}_{q}(s)\sim {s}^{h(q)}$$

(8)

The function h(q) is generalized Hurst exponent.

Step 6: Eq. (8) can be rewritten as ${F}_{q}\left(s\right)={AS}^{h(q)}$. After taking logarithms on both sides, we have:

$$\mathrm{log}{F}_{q}(s)=\mathrm{log}A+h(q)\mathrm{log}s$$

(9)

We finally determine the scaling behavior of the fluctuation functions by analyzing the log–log plot of the all the ${Fq}_{(s)}$ versus $s$. If the original series of ${x}_{i}$ values has long range correlations, there exists a range of scales, ${s}_{\mathrm{min}}<s<{s}_{\mathrm{max}}$, in which ${F}_{q}(s)\sim {s}^{h(q)}$ where h(q) is the generalized Hurst exponent and it can be estimated as the slope of the log–log plot of ${Fq}_{(s)}$. If the series is monofractal and stationary, then, h(q) is equal to the Hurst exponent h, i.e., independent of q. Otherwise, for a multifractal time series, the generalized Hurst exponent is a decreasing function of q.

From Eq. (6) we can define the level of efficiency as:

$$ \Delta h = \max \left[ {h\left( q \right)} \right]{-}\min \left[ {h\left( q \right)} \right] $$

(10)

The higher the values of “∆h”, the lower the price efficiency of a time series.